2. YEDITEPE UNIVERSITY ENGINEERING FACULTY
MECHANICAL ENGINEERING LABORATORY
1. OBJECTIVE
To calibrate the system with a known viscosity.
To measure fluid viscosity and observing the difference between Newtonian and non-
Newtonian fluids.
2. EQUIPMENT
Capillary tube
Multimeter
Pressure Sensor
Compressor
Thermometer
Beaker
Pressure Tank
Stop-watch
Water container (the cup that capillary tube is connected)
Electronic balance
Power Supply
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3. 3. PROCEDURE
Water
Tank
Cappilary
Tube
Figure 1: Schematic diagram of the test setup
3.1 Calibration of the capillary tube
1. Fill the beaker with tap water and measure its temperature by using a thermometer.
2. Poor the tap water into the water tank and close the lid of the capillary tube.
3. The beaker is weight.
4. Prepare the stop-watch and place the beaker under the capillary tube.
5. Measure the initial height of the fluid (H1) and record it.
6. Simultaneously open the lid of the capillary tube and start the stop-watch.
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4. 7. When water level drops to a specific height (do not allow the water completely flow
through the tank stop the experiment before it completely finishes) stop the stop-watch
and measure the final height of the fluid. Record the height and time measured by the
stop-watch.
8. Weigh the beaker (this time with the water in it!) and determine the mass of the water by
subtracting the empty weight of the beaker measured in the step 3. Than record it.
9. Repeat steps 2 times.
10. Use measurements to calculate capillary tube diameter according to Eq. 4.4 via the
computer software and compare result with the known value.
3.2 Measuring the viscosity of the water and peach juice
1. Fill the beaker with tap water and measure its temperature by using a thermometer.
2. Poor the tap water into the water tank and close the lid of the capillary tube.
3. The beaker is weight.
4. Check that valve 1 is open and valve 2 is closed shown in Fig 1.
5. Fill the pressure vessel with pressurized air from the compressor until the pressure in the
compressor air tank reaches to 0.2 bars (run the compressor until this moment than stop
it).
6. After stopping the compressor you will see that the pressure is balanced between
compressor and pressure vessel and the final value will be 0.4 bars.
7. Prepare the stop-watch and place the beaker under the capillary tube.
8. Measure the initial height of the fluid (H1) and record it.
9. Open the valve 2 and valve 3 shown in Fig. 1.
10. Measure the ampere (A1) from the multimeter and record it.
11. Simultaneously open the lid of the capillary tube and start the stop-watch.
12. When water level drops to a specific height (do not allow the water completely flow
through the tank stop the experiment before it completely finishes) stop the stop-watch
and measure the final height of the fluid (H2) and the final ampere (A2). Record the
height and time measured by the stop-watch.
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5. 13. Weigh the beaker (this time with the water in it!) and determine the mass of the water by
subtracting the empty weight of the beaker measured in the step 3. Than record it.
14. Repeat steps 2 times.
15. Use measurements to calculate viscosity of the fluid by using Equation 4.2 and compare
the results by known value.
16. Repeat all steps for peach juice
4. THEORY
A fluid has an ability to flow by changing positions of its molecules with respect to
another. As expected this ability to flow is different for different fluids. As an example from real
life: if you poor a cup of water and honey on a surface it is seen that water flows easier than the
honey. This is because viscous effects on honey are much bigger than viscous effects on water.
There two related measures of fluid viscosity. These are known as the dynamic (absolute)
viscosity and the kinematic viscosity. Dynamic viscosity, μ, is the measure of the internal
resistance. It is the tangential force per unit area that required for the movement of the fluid layer
with respect to the neighboring one at unit displacement for a unit velocity. Kinematic viscosity,
υ, is the ratio of the dynamic viscosity to density of the fluid. No force is applied in this quantity.
It is expressed as υ = μ/ρ. Velocity gradient and stresses effecting on the fluid flowing in the pipe
is given in Fig. 2
Figure 2: Velocity is zero on the wall of the pipe as no slip condition states. Also it is seen that velocity
increases as y reaches to the middle of the pipe and gets its highest value.
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6. 2.1. Newtonian and Non-Newtonian fluids
When shear stress applied, viscosity of some fluid change. These types of fluids are
called as Non-Newtonian fluids. Non-Newtonian fluids can be categorized as shear-thinning and
shear thickening. Fluids that have no change in their viscosity by an applied shear stress are
called as Newtonian fluids. As an example mixing the fluid by a spoon or applying pressure on
the fluid creates shear stress on the fluid.
Shear thinning:
Shear thinning liquids have macromolecules or particles. And these molecules are
randomly stayed together under no flow. But at large shear stress levels they start to orient
themselves to the flow and their molecules rotate become parallel to the flow. Shear thinning
liquids’ viscosity decreases as the shear force increases.
Shear thickening:
Shear thickening liquids usually have solid particle suspensions. At low shear the fluid
layers act like a thin film layer to the relative motion and viscosity is low too. Contrary to shear
thinning liquids when the shear stress is increased the particle to particle contact and friction
appears. Thus the viscosity of shear thickening liquids increases as the shear force increases.
Figure 3: Viscosity vs. Shear Rate
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7. 2.2 Reynolds Number
In fluid mechanics Reynolds number, which is a dimensionless number, shows the
behavior of the flow. It is literarily the ratio of internal forces to viscous forces. Also it refers to
the flow situations, relative motion of the fluid, in various conditions. Reynolds number is given
as the following;
(4.1)
Where;
Re Reynolds number
ρ Fluid density
L Characteristic length
u Velocity of the fluid
μ Viscosity of the fluid
The flow type of the fluid should be known to make further calculations for the fluid viscosity.
For a flow through a pipe, the flow is
Laminar when Re < 2300
Transient when 2300 < Re < 4000
Turbulent when Re > 4000
2.3 Equations for Calculations
The viscosity of the fluid is calculated by using equation which is given below. This
equation is used only for the laminar flow condition.
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8. ̇
( ) ( ) {( ) } (4.2)
̇ ̇
Where;
ρ Fluid density
L Length of the capillary tube (thickness of the connection member is included)
̇ Mass flow rate
g Gravitational acceleration
Pt Applied pressure
Pa Atmospheric pressure
D Diameter of the capillary tube
Ht Average of the initial height and the final height of the fluid ( )
α2 Kinetic energy correction factor for fully developed laminar flow
Kent Entrance loss
Output of the pressure sensor is milliampere which is 4-20mA.Range of the pressure sensor is 0-
10psi (0-0.69bar). The applied pressure is obtained from equation which is given below;
( ) (4.3)
Pt Applied pressure
Aave Average milliampere which is read from multimeter ( )
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9. The diameter of the capillary tube is calculated by doing algebraic arrangements to above
equation as follows.
̇ ̇
( )
( ( ) ( ( ))
) (4.4)
Take Kent, α2 and μ (water) as following for the calculations.
Kent=0.24
α2 =2
μ water = 0.0010449 ( )
Shear stress on the pipe wall can be found by using equation 4.5.
̇
(4.5)
The following “Figure 4” is the graph of the ( ) - ( )for ketchup. The coefficient of
x in the graph (can be denoted as n) is found as 0.3089. The reason of taking the logarithm of the
“ ” and “ ” is very important.
If
n<1 the fluid is Non-Newtonian
n>1 the fluid is Newtonian
Where;
V Fluid velocity
D Diameter of the capillary tube
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10. Figure 4: The slope of the line on the ( ) and ( ) plot shows if the fluid is shear thinning
or shear thickening.
5. ANALYSIS AND DISCUSSION
1. Give a sample calculation of the diameter, the viscosity, and the wall shear stress.
2. Show the variations of the ( ) (in x axis) - ( ) (in y axis) for each fluid in
the different graphs and comment the graph.
3. Discuss how the viscosity changes with τ wall.
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